A comprehensive 10-page probability cheatsheet that covers a semester's worth of introduction to probability.
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update stationary distribution of Markov Chain
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This cheatsheet is a 10-page reference in probability that covers a semester's worth of introductory probability.

The cheatsheet is based off of Harvard's introductory probability course, Stat 110. It is co-authored by former Stat 110 Teaching Fellow William Chen and Stat 110 Professor Joe Blitzstein.



First Page Second Page


This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License..

Creative Commons License

Planned Additions

  • Monty Hall
  • St. Petersburg Paradox


2.0 / 2015-09-04

Contributor: Joe Blitzstein

Summary: A huge thanks goes to Professor Joe Blitzstein (@stat110) for his work in polishing up the cheatsheet, adding colors and figures, and officially using it in his Stat 110 class (which is the class that inspired this cheatsheet to begin with). The cheatsheet is now a joint work by William and Professor Blitzstein.


  • Figures
  • Probability of an Intersection or Union
  • Distributions in R Section
  • Colors


  • Extensive polishing and rephrasing for clarity, consistency, and quality.


  • Inequalities moved from the back reference sheet to inside the cheatsheet under "Distribution Properties"
  • Some sections reordered


  • Repeated definitions of PMF and CDF
  • Calculating Probability (2) from Example Problems
  • MGF -- Distribution Matching from Example Problems

1.1.1 / 2015-03-20

Summary: Cleaned up sections, moved things around to more logical locations, and fixed one error in formula. Also removed some left margins, which allowed room for a Settlers of Catan diagram and the hat-matching problem.


  • Settlers of Catan diagram
  • Hat-matching problem


  • Unused theorems and commands
  • Left margins on descriptions

Major Fixes

  • Fixed error in Law of Total Probability formula


  • Classic Problems is now merged into Example Problems


  • Reorganized material on Beta distribution

1.1 / 2015-02-28

Summary: Added a new page of content, including vast improvements to problem solving solutions and a new biohazards section.


  • Probability that the normal distribution falls in a certain interval
  • Convolutions section
  • Minimum and Maximum of Random Variables problem
  • Adam and Eve's Laws problem
  • MGF - Distribution Matching problem
  • Two Markov Chain problems
  • Major improvements to Problem Solving Strategies
  • Biohazards Section
  • Recommended Resources Section)


  • Duplicate Law of Total Expectation section


  • Amoeba Spliting and Typos in your Textbook to Example Problems

Major Fixes

  • Fixed solution to "Orderings of i.i.d. random variables"

1.0 / 2014-07-13


  • Probability Cheatsheet

Contact Us

For comments, suggestions, and corrections: contact William, submit a pull request, or submit an issue on Github!

William Chen - You can message William on Quora, tweet him at @wzchen, or contact him via his website

Joe Blitzstein - You can tweet Joe at @stat110